Charge Polarization and Current Distribution in a Conductive Particle in the Rayleigh Region

Abstract

An investigation of the interaction of a conductive sphere with an electromagnetic wave with attention given to space-charge effects would appear timely, as there is much current interest in the electromagnetic properties of mesoscopic structures. In this study, the polarization of a small semiconductor sphere immersed in a dynamic electric field is explored analytically and numerically. In one approach, suitable for a sphere with low to moderate charge carrier concentration, the Poisson's equation is coupled with the transport equations of the carriers, leading to a quasi-static formulation under the weak-field approximation. Screening effects of the charges on the interior field are revealed, along with a current distribution that is essentially uniform over much of the volume of the sphere. Frequency dependence of the total induced dipole moment of the sphere displays strong dispersion and absorption near the bulk plasma frequency. Validity of the quasi-static assumption is assessed by comparison to results of calculations based on a full-wave formulation. As the nominal carrier concentration exceeds 1020 cm-3, the quasi-static solutions for interior field and current distribution begin to deviate from the full-wave solution and the latter must be employed to provide a realistic account of the charge-wave interaction within the sphere.